Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

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This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation u k is strongly mixing. More precisely a r is a periodic sequence of real numbers with period P 0 and such that P r=1 |a r | 1. The time series u r is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated.